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					    Interstitial aggregates and a new model for the I1 /W optical

                                        centre in silicon

                                                            ¨
               B. J. Coomera , J. P. Gossa , R. Jonesa , S. Obergb , P. R. Briddonc
                a School   of Physics, The University of Exeter, Exeter EX4 4QL, UK
           b Department                                        a,    a
                             of Mathematics, University of Lule˚ Lule˚ S-97187, Sweden
c Department   of Physics, The University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU,

                                                  UK

                                           (August 3, 1999)




                                             Abstract

           First principles local-density-functional (LDF) theory is employed to in-

          vestigate the properties of di-interstitial (I2 ), tri-interstitial (I3 ) and tetra-

          interstitial (I4 ) structures in silicon. We show that a tri-interstitial defect can

          account for many of the fundamental properties of the I1 /W-optical centre

          which is observed in irradiated, annealed silicon.




   Keywords: silicon, W-line, interstitial, aggregation




   Name and contact information of corresponding author:


B. J. Coomer
School of Physics

Stocker Road
The University of Exeter


                                                   1
Exeter EX4 4QL
UK


Ph. +44 1392 264198
Fax +44 1392 264111
e-mail: coomer@excc.ex.ac.uk
   It is well known that following the annealing of electron or ion irradiation of silicon

or germanium, extended structures are generated that are observable with transmission-
electron-microscopy (TEM). These ‘rod-like’ defects lie along [110] on a {311} habit-plane.
The proposed model [1] is that of a [110] chain of self-interstitials which is inserted down a
[110] channel. The TEM results are well matched by this model if a bonding rearrangement
on both sides of the chain is included. This ‘bond-switching’ process has been shown to

significantly lower the energy of the extended structure [2].
   In contrast to the wealth of information on the extended defects, there is little published
data concerning the first stages of the aggregation process of self-interstitials. One assign-
ment has been made of a di-interstitial structure to the electron paramagnetic resonance

(EPR) spectrum, P6 [3]. However, this model is not universally accepted.
   The I1/W-optical centre is observed in silicon which has been exposed to lattice damaging
treatments with subsequent annealing at around 500 K. It is seen in both n- and p-type silicon
following self-ion irradiation [4]. The centre is characterised by a sharp peak at 1018.2 eV and

an associated phonon sideband, containing local vibrational modes (LVMs). Uniaxial stress
measurements reveal the defect symmetry to be trigonal. Although this intriguing centre
has received much attention by both experimentalists and theorists, a definitive model is
still lacking.
   It is generally accepted that the W-centre arises from the agglomeration of an intrinsic

species. Much work in the past has concentrated on the defect being vacancy related [5–7]
but more recent experiments [4,8,9] have supported the interstitial nature of the W-centre.
We review this information now:


                                               2
  1. The LVM detected in luminescence, with energy 70.0 meV is consistent with a strength-
     ened Si–Si bond. Calculations [10] have shown that the optimisation of vacancy defects
     leads to the lengthening of Si–Si bonds and such defects could not give rise to local

     modes lying above the Raman frequency [8].

  2. The stress response of the W-optical line is two orders of magnitude smaller than that
     of the 1039 meV line in silicon which is believed to be a vacancy aggregate [8]. Also the
     shift of the W-luminescence line with stress is very much smaller than that of V6 (the
      4
     B80 luminescence centre) [11,12]. Analysis of the W-vibronic sideband suggests that
     the W-defect is less compressible than bulk Si [8]. Such a low stress response would
     be expected for an interstitial defect where bonds are compressed.

  3. The release of interstitials from irradiation damage regions during annealing has been

     tentatively correlated with the growth of the W-centre [13].

  4. Although the existence of the W-centre is not dependent on the presence of any im-
     purity, the effect of carbon and oxygen impurities on the defect concentration has also
     been used to argue that the defect is interstitial related [9].

   Following annealing at around 500 K of He, Ne, Ar or Kr ion-bombarded silicon, a new
family of trigonal centres are observed. Although the new zero-phonon lines and associated
LVM sideband structures are qualitatively the same as the W-centre, the system is red-
shifted by between 1–10 meV, depending upon the identity of the noble-gas atom. The

one-phonon replicas of the noble-gas related defects are also shifted slightly relative to the
W-centre one-phonon replica. Davies et al [8] claims that this effect is consistent with a
strain interaction between the noble-gas atom and the W-centre, i.e., the noble-gas atom
lies close to the W-centre and, although no chemical bonding takes place, the presence of
the noble-gas atom perturbs the electronic and geometric structure of the W-centre.

   Comprehensive studies of Ar ion-beam etched silicon [14] have indicated that an un-
expected and enhanced diffusion process takes place before the W-like defect forms. The


                                              3
observed depth profile of the noble-gas related centres suggests that the argon atoms are
penetrating deeper into the sample than expected – up to 1 µm. The diffusion co-efficient
was estimated to be D = 5 × 10−14 cm2 s−1 . Using D = νa2 eEb /kT where ν is the attempt

frequency (∼ 1013 Hz) and a is the diffusion length (∼ 3.0 ˚), this leads to a barrier height
                                                          A
of Eb =0.65 eV. Implantation [15] and permeation [16] studies show that helium diffuses with
an activation energy between 0.8 and 1.3 eV. Since the argon atom has almost twice the
covalent radius of He, one would expect the diffusion barrier of Ar to be significantly greater

than 0.65 eV.
   Although it is thought that the thermal migration barrier for the self-interstitial is greater
than 1 eV, the interstitial has been observed to undergo an enhanced diffusion at cryogenic
temperatures [17]. Recent studies of irradiated silicon [18] have obtained a value of 0.065 ±

0.015 eV for the migration energy of the silicon self-interstitial under ionising conditions.
Therefore, the anomalous diffusion of Ar could be explained by an interstitial mechanism if:

 (a) A binding energy exists between the isolated self-interstitial and the noble-gas atom.

 (b) The presence of the self-interstitial significantly reduces the energy required for the
      noble-gas atom to move through the lattice.

   It has also been suggested [7] that the enhanced diffusion of the noble-gas atom could
be due to repulsion from a wave of vacancies released during implantation. However, a
microscopic model for this process has not been put forward.

   We present the results of state-of-the-art calculations investigating the structures and
electronic properties of interstitial defects. The properties of the lowest energy tri-interstitial
are compared with the W-optical centre.
   A local density-functional (LDF) code (aimpro [19]) is used. Large, hydrogen terminated

clusters are used with composition Si181+n H116 (n = 2, 3, 4) to investigate the interstitial
defects. Several models for I2 and I3 are compared in energy. For I4 , the structure proposed
by Aria et al [20] is optimised. The total energy of the structure is compared with a [110]
interstitial-chain element. The positions of all the Si atoms were optimised using a conjugate

                                                4
gradient method. Electrical levels were calculated using a transition-state method described
elsewhere [21].
   Several structures were considered for I2 . Two similar structures [22,23] were found

lowest in energy and both consist of three Si atoms sharing a single substitutional site. The
lowest energy form of this type of I2 defect was found to possess C1h symmetry (see Fig. 1).
In this case the two interstitial atoms lie along [110] [23]. Two other structures were found
to lie around 0.4 eV higher in energy. The first is formed by placing two parallel [100] split-

interstitials at next-nearest-neighbour sites. The second is formed by placing the additional
atoms in opposing bond-centred sites either side of a hexagonal ring. Both structures include
two atoms which are 3-fold coordinated, all other atoms being fully coordinated. The model
assigned by Lee [3] to the P6 EPR centre was calculated to lie ∼ 3.0 eV higher in energy

with the symmetry constrained to D2d . Removal of symmetry constraints results in a new
structure and an energy lowering of 1.1 eV. However, the resultant defect has little in common
with the ground state structure proposed by Lee.
   The lowest energy tri-interstitial investigated possesses C3v symmetry. The structure

is formed by placing each additional Si atom at the centre of three parallel bonds which
surround a tetrahedral interstitial site (see Fig. 2). Structural optimisation of this structure
involves the formation of a three-atom ring resulting in full four-fold coordination of all
atoms. The optimisation was repeated from an asymmetric starting configuration resulting
in the same relaxed structure. It is interesting to note that this structure is a three atom

section of a [110] interstitial-chain which is a basic element of the {311} planar defects
observed following high temperature annealing of irradiated silicon [1].
   The electrical levels of the tri-interstitial were calculated. The defect does not appear to
possess an (−/0) acceptor level but a possible (0/+) donor level was calculated to lie close

to the valence band edge (∼ Ev + 0.1 eV).
   The I3 defect possesses a number of LVMs. A symmetric vibrational mode lies at 74 meV,
consistent with experiment (70.0 eV). This mode is localised upon unique atoms lying on the
principal [111] axis of the defect. The mode shifts by 12 cm −1 when one atom is replaced by

                                               5
30
     Si, which is in reasonable agreement with the experimentally observed shift of 16 cm−1 [8].
      A slightly enlarged interstitial cage lies along the principal [111] axis of the tri-interstitial,
providing a possible site for noble-gas atoms. The effect of placing an argon atom at this site

is to perturb the electronic structure of the tri-interstitial and enlarge the cage surrounding
the argon atom. The bond which gives rise to the 74 meV symmetric mode is only slightly
perturbed by the presence of the argon. To show that the trigonal symmetry structure was
a local minimum, the argon was displaced from its optimised trigonal axis site by ∼ 1.0 ˚.
                                                                                        A

In the subsequent optimisation the Ar relaxed back to the high symmetry site.
      Two I4 models were optimised. The model suggested by Aria et al [20] was found to be
significantly lower in energy than a 4-atom [110] interstitial chain element. The optimised
structure (Fig. 3) compares well with that calculated by Aria et al. All atoms are 4-fold

coordinated with bond lengths and bond angles distorted from their ideal values by no more
than ∼10%. The calculations suggest that the (-/0) and (0/+) levels lie within 0.1 eV of Ec
and Ev respectively.
      In conclusion, we propose a new model for the tri-interstitial in silicon. Its calculated

properties agree well with experimental information on the W-optical centre. The structure
is closely related to the {311} defect structure proposed by Takeda et al [1]. We propose a
suitable site for a noble-gas atom nearby the tri-interstitial. This structure gives rise to the
correct symmetry and the inert-gas atom is expected to perturb the W-centre as observed.
      Energy comparisons between di-interstitial defects reveal four low energy structures

within 0.5 eV of each other. Optimisation of the [100] oriented I4 structure results in a
geometry close to that reported in the previous theoretical calculations of Aria et al. Elec-
trical level calculations show that the defect is unlikely to introduce deep levels into the
band-gap.


                                     ACKNOWLEDGMENTS


         ¨
      S. O. thanks NFR and TFR for financial support. We also thank the ENDEASD network.


                                                    6
                                    REFERENCES

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 [7] S. K. Estreicher, J. Weber, A. Dereckei-Kovacs and D. S. Marynick, Phys. Rev. B 55,

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 [8] G. Davies, E. C. Lightowlers and Zofia E. Cienchanowska, J. Phys. C: Solid State Phys,
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 [9] M. Nakamura, S. Nagai, Y. Aoki and H. Naramoto, Appl. Phys. Lett. 72, 1347 (1998).

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[10] B. J. Coomer, A. Resende, J. P. Goss. R. Jones, S. Oberg and P. R. Briddon, Physica
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[11] A. S. Kaminskii and E. V. Lavrov, Solid State Commun. 106, 751 (1998).

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[12] B. Hourahine, R. Jones, A. N. Safonov, S. Oberg, P. R. Briddon, and S. K. Estreicher,
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[13] H. Feick and E. R. Weber, Physica B, this edition.

[14] J. Weber, Physica B 170, 201 (1991).

[15] P. Jung, Nuc. Inst. and Methods in Phys. Res. B 94, 362 (1994).

[16] A. Van Wieringen and N. Warmholtz, Physisca XXII, 849-865 (1956).


                                            7
[17] G. D. Watkins, in Radiation Damage in Semiconductors (Dunod, Paris, 1964, p. 97.

            e
[18] A. Hall´n, N. Keskitalo, L. Josyula and B. G. Svensson, J. App. Phys 86, 214 (1999).

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                              ¨
[21] A. Resende, R. Jones, S. Oberg, P. R. Briddon, Phys. Rev. Lett. 82, 2111 (1999).

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[23] S. K. Estreicher, Hydrogen ’99 workshop, Exeter University (1999).




                                             8
                                             FIGURES



   FIG. 1. Optimised structure of the lowest energy form of I2 investigated. Three Si atoms share

a single substiutional site. The two interstitial atoms lie along [110] as indicated.




   FIG. 2. (a) A section taken from the ideal diamond structure. To form the tri-interstitial,

additional atoms are placed at the bond-centred sites indicated by the black circles. The bond

reconstruction that results from the structural optimisation is indicated by the dashed lines (b)

The fully optimised structure. A possible site for a noble-gas atom is along [¯¯¯ in the cage
                                                                              111]

adjacent the 3-atom ring




FIG. 3. Optimised structure of I4 . Distortions from the ideal bond lengths and angles are shown.




                                                  9
     [110]




10
(a)           (b)



      [111]




       11
          c
                                                    c
 b                    b                1% +1.0o
                                          -2.
      a               a           b -13.9 o                     b
 a                a
                                      -0.3 o




                                 -5.
                                    2%
                                            -1.5%
                                           a                a
a a                                        -4.4 o




                                      %
                      a a




                                  -2.7
              b                           o
      b                           a -12.6                       a
                                          -4.           o
          c                                  4% -7.1
                                                    b




                            12